Let's solve each part of the problem step by step.

Given Data:

Jordan's monthly electric bills for the past 10 months are: $115, 150, 144, 126, 90, 90, 95, 110, 120, 88$

a. Mean Monthly Electric Bill

The mean is calculated by summing all the bills and dividing by the number of months.

$\text{Mean} = \frac{115 + 150 + 144 + 126 + 90 + 90 + 95 + 110 + 120 + 88}{10}$ $\text{Mean} = \frac{1128}{10} = 112.80$

So, the mean monthly electric bill is $112.80.

b. Range

The range is the difference between the highest and lowest bill.

$\text{Range} = 150 - 88 = 62$

So, the range of the electric bills is $62.

c. Variance

The variance is calculated using the formula:

$\text{Variance} = \frac{1}{N} \sum_{i=1}^{N} (x_i - \text{Mean})^2$ Where $N$ is the number of bills (10 in this case), and $x_i$ is each bill.

1. Calculate the squared differences: $(115 - 112.80)^2 = 4.84$ $(150 - 112.80)^2 = 1379.84$ $(144 - 112.80)^2 = 968.64$ $(126 - 112.80)^2 = 173.44$ $(90 - 112.80)^2 = 523.84$ $(90 - 112.80)^2 = 523.84$ $(95 - 112.80)^2 = 319.84$ $(110 - 112.80)^2 = 7.84$ $(120 - 112.80)^2 = 51.84$ $(88 - 112.80)^2 = 620.64$

2. Sum of squared differences: $4.84 + 1379.84 + 968.64 + 173.44 + 523.84 + 523.84 + 319.84 + 7.84 + 51.84 + 620.64 = 4574.76$

3. Divide by the number of bills to find the variance: $\text{Variance} = \frac{4574.76}{10} = 457.48$

So, the variance of the electric bills is $457.48.

d. Standard Deviation

The standard deviation is the square root of the variance:

$\text{Standard Deviation} = \sqrt{457.48} \approx 21.39$

So, the standard deviation of the electric bills is $21.39.

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If you have any questions or need further details, feel free to ask. Here are five related questions to consider:

1. How would the mean change if the highest bill was $160 instead of $150?
2. What impact would doubling all bills have on the variance and standard deviation?
3. How does the standard deviation help in understanding the variability of Jordan's electric bills?
4. What would the range be if the lowest bill was $80 instead of $88?
5. How would the variance change if we excluded the highest and lowest bills?

Tip: Understanding the variance and standard deviation helps in assessing the consistency of monthly expenses.